12 Jan 27: Density dependence (discrete time)

Density-yield and discrete time density dependence

12.1 Required reading

Vandermeer, J.H., Goldberg, D.E., 2013. Population Ecology: First Principles (Second Edition). Princeton University Press, Princeton, United States. p17-19 and 28-29. Link

There are also slides on BrightSpace: Additional resources > Density Dependence DT.pdf

12.2 Questions

1. Logistic growth assumes density dependence in the population growth rate. This, however, may be insufficient in many applications. In the section, The Yield-Density Relationship what solution is proposed?

2. As written in Vandermeer and Goldberg the Shinozaki-Kira equation is presented without an =. Write the complete equation, by adding in an equals and quantity on the other size of the equals. Define all the parameters and variables in the equation.

3. The Beverton-Holt equation is equation (28) on p29. There are two values of \(N_t\) such that \(N_t = N_{t+1}\). One value can be found by re-arranging,

\[ 1 = \frac{\lambda}{1+\alpha N_t}, \]

until \(N_t\) is isolated on one side. To find the other value inspect the equation,

\[ N_{t+1} = \frac{\lambda N_t}{1+\alpha N_t}. \]

What is another value of \(N_t\) such that \(N_{t+1}=N_t\).